Question

Select the angle that correctly completes the law of cosines for this angle

Answer 1

Answer: Option A.

Step-by-step explanation:

1. By definition the law of cosine is:

$c^{2}=a^{2}+b^{2}-2ab cos(C)$

2. By definition, the angle $C$ is opposite to the side whose length is $c$.

3. Then, as you can see in the figure attached in the problem the length of the side c is:

$c=12$

3. Therefore, you can conclude that the measure of the angle $C$ is 67°.

4. To verify you can solve for the angle, as following:

$12^{2}=5^{2}+13^{2}-2(5)(13)cos(C)\\\\-12^{2}+5^{2}+13^{2}= 2(5)(13)cos(C)\\\\\frac{-12^{2}+5^{2}+13^{2}}{2(5)(13)} = cos(C)\\\\arcos(\frac{-12^{2}+5^{2}+13^{2}}{2(5)(13)}) = C\\C=67\°$

Then, the answer is the option A.

Answer 2

Answer

A

Step-by-step explanation:

Correct answer is A